In Europe at least I'd expect it to be a total non-starter.
For starters, there's a ton of alternatives, but more importantly giving out the debit card number is high risk - much worse even than handing out your credit card details (getting charges dropped / charged back is much more effort with a debit card) - whereas giving out your bank account details is not (if bank lets anyone do anything other than depositing money in your account with just your account details, the liability is entirely on them).
And for most transfers within the EU, you can do an online electronic transfer and get the money to the recipient in <2 hours - very often in less than 10 minutes.
Same in Australia. It always amazes me how archaic the US banking system is - particularly the continued use of checks. When my wife (then girlfriend) saw that I owned a check book here in Oz she burst out laughing and called me an old man. That was a decade ago.
For starters, there's a ton of alternatives, but more importantly giving out the debit card number is high risk - much worse even than handing out your credit card details (getting charges dropped / charged back is much more effort with a debit card) - whereas giving out your bank account details is not (if bank lets anyone do anything other than depositing money in your account with just your account details, the liability is entirely on them).
And for most transfers within the EU, you can do an online electronic transfer and get the money to the recipient in <2 hours - very often in less than 10 minutes.